7561 ÷ 8 = 945 R1
Alright, let's work through the division of 7561 by 8 step by step.

Step 1:
8 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 7 to get 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 8

Step 2:
8 goes into 75 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 72 from 75 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 8

Step 3:
8 goes into 36 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 94
Subtract 32 from 36 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 8

Step 4:
8 goes into 41 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 945
Subtract 40 from 41 to get 1.

The final result is 945 with a remainder of 1.